 # Statistics Problem: Agriculture Department

Subject Mathematics General Statistics

## Question

The Agriculture Department of a certain country reported that the average coffee consumption in the country, in 2014, was 26.0 gallons per person. A recently taken random sample of 400 residents of the country found a mean coffee consumption of 26.7 gallons with a sample standard deviation of 6.8 gallons. Assuming that the population of coffee consumption is normally distributed, test, at the 10% level of significance, whether the mean coffee consumption is different from the reported 26.0 gallons, by answering the following:

(a) State the null and alternative hypotheses for the test.
(b) Calculate the test statistics.
(c) Determine the rejection region(s) for the test.
(d) State the conclusion for the test giving reasons for your answer.

## Solution Preview

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C) By splitting our alpha level, .1, into two-tails (because our hypothesis test involved an equality/inequality relationship), then each tail would equal z=.05 – which corresponds to values of 1.645 and -1.645.
D) Since our z-value (2.059) falls within the right-tail critical region, we are able to reject the null hypothesis and thus accept the alternative hypothesis. In other words, the average coffee consumption was not 26 gallons per person....

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